Karim Soltan is shopping for a new vehicle, and has noticed that many vehicle manu-facturers are offering special deals to sell off the current year’s vehicles before the new models arrive. Karim’s local Ford dealership is advertising 3.9% financing for a full 48 months (i.e., 3.9% compounded monthly) or up to $4000 cash back on selected vehicles. The vehicle that Karim wants to purchase costs $24 600 including taxes, delivery, licence, and dealer preparation. This vehicle qualifies for $1800 cash back if Karim pays cash for the vehicle. Karim has a good credit rating and knows that he could arrange a vehicle loan at his bank for the full price of any vehicle he chooses. His other option is to take the dealer financing offered at 3.9% for 48 months. Karim wants to know which option requires the lower monthly payment. He knows he can use annuity formulas to calculate the monthly payment. Question  Suppose Karim decides to explore the costs of financing a more expensive vehicle. The more expensive vehicle costs $34 900 in total and qualifies for the 3.9% dealer financing for 48 months or $2500 cash back. What is the highest effective annual rate of interest at which Karim should borrow from the bank instead of using the dealer’s 3.9% financing?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Karim Soltan is shopping for a new vehicle, and has noticed that many vehicle manu-
facturers are offering special deals to sell off the current year’s vehicles before the new models
arrive. Karim’s local Ford dealership is advertising 3.9% financing for a full 48 months (i.e.,
3.9% compounded monthly) or up to $4000 cash back on selected vehicles.
The vehicle that Karim wants to purchase costs $24 600 including taxes, delivery, licence,
and dealer preparation. This vehicle qualifies for $1800 cash back if Karim pays cash for the
vehicle. Karim has a good credit rating and knows that he could arrange a vehicle loan at his
bank for the full price of any vehicle he chooses. His other option is to take the dealer financing
offered at 3.9% for 48 months.
Karim wants to know which option requires the lower monthly payment. He knows he can
use annuity formulas to calculate the monthly payment.

Question 

Suppose Karim decides to explore the costs of financing a more expensive vehicle. The
more expensive vehicle costs $34 900 in total and qualifies for the 3.9% dealer financing
for 48 months or $2500 cash back. What is the highest effective annual rate of interest at which Karim should borrow from the bank instead of using the dealer’s 3.9% financing?

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